The Ehrenfest model for heat exchange can be described as follows: Two urns, A and B, contain a total of 2N balls. At every step, one ball is equally likely to be drawn from among all 2N balls. It is then put into the other urn. Let Xn be the number of balls in urn A immediately after the nth step. Goldenberg (1988) uses this chain to represent futures and security prices, which tend to return to an equilibrium N. The greater the distance between the current price and N, the greater the probability that it moves toward N rather than away from it. Required:
Find the transition matrix for this process.